A new definition of fractional derivative

By Roshdi Khalil, M. Horani, Abdelrahman Yousef, M. Sababheh. Journal of Computational and Applied Mathematics, 2014

3,178 citations recorded by the source corpus.

Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/6dcc7431b4a339c0209979a6b17feb61fcba4072

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In Applied Mathematics

In Modeling and Simulation

In Numerical Analysis

Citations in the corpus

On a Fractional Operator Combining Proportional and Classical Differintegrals (2020, background): “The so-called conformable derivative was presented in [13] in 2014 as a local, limit-based definition.”
A new truncated $M$-fractional derivative type unifying some fractional derivative types with classical properties (2017, background): “[7], the alternative fractional derivative and the generalized alternative fractional derivative proposed by Katugampola [8] and the M -fractional derivative proposed by Sousa and Oliveira [9], with our truncated M -fractional derivative type.”
Modified Auxiliary Equation Method versus Three Nonlinear Fractional Biological Models in Present Explicit Wave Solutions (2018, neutral): “u(x, y, t) = √ s √ β2 − 4ασ β− 4α2 β + √ β2 − 4α2 tanh ( −2λ √ stκ+μ √ β2−4α2(xκ+iyκ) 2κ )  , (23)”
The flaw in the conformable calculus: It is conformable because it is not fractional (2018, background): “proposed a definition for the fractional derivative in [5] using what they called the “conformable derivative”.”
Integration by parts and its applications of a new nonlocal fractional derivative with Mittag-Leffler nonsingular kernel (2016, methodology): “For the nonlocal fractional derivatives with nonsingular exponential kernel we refer to [19, 20] and for other local approaches of the fractional derivatives we refer to the recent manuscripts [21, 22].”
Three-Point Boundary Value Problems for Conformable Fractional Differential Equations (2015, background): “The conformable fractional derivative aims at extending the usual derivative satisfying some natural properties (see [1]) and gives a new solution for some fractional differential equations.”